Directed Graph Model Research Articles

Graph total variation and low-rank regularization for heterogeneous change detection

Heterogeneous change detection (HCD) is challenging because different imaging mechanisms for various sensors make images difficult to compare directly. To address this problem, a graph-based regression algorithm is proposed for HCD, by leveraging the Graph Total Variation regularization and Low-Rank matrices decomposition (GTVLR). Utilizing graph signal processing (GSP) theory, a directed graph (digraph) model is employed to effectively represent the orientation and correlation information of images, thereby enabling direct comparison of heterogeneous data within the same domain after graph filtering. The GTVLR framework facilitates the decomposition of post-event images into regression and changed images. This decomposition ensures that the regression image mirrors the structure similarity of the pre-event image, while the changed image highlights areas of alteration, aiding in change detection. The model characterizes the piecewise smoothness and Low-Rank properties of data through GTV regularization and Low-Rank penalty, respectively. Moreover, by integrating the higher-order neighboring information within the digraph to refine the model. Experiments conducted on three real-world datasets and comparison with several state-of-the-art methods demonstrate the effectiveness of the proposed algorithm.

Inverse system based decoupling design and control strategy for crude oil heat exchanger networks

This work focuses on a decoupling control approach for the crude oil heat exchanger network to improve the energy efficiency and achieve continuous energy saving. The desired control variables are identified by the signed directed graph (SDG) model based on the complex network theory. Then the principal component analysis (PCA) method and the evaluation index are employed to construct the initial controller as well as the control variables pairing. The presented system is a multi-input multi-output (MIMO) control system where the coupling problems are considered, and a decoupling control strategy based on the inverse system theory of neural network is proposed. The existence of the inverse system is proved by the reversibility derivation, and the original system is decoupled into two second-order subsystems. Consequently, the proposed decoupling control system is tested on the example of heat exchanger network (HEN) belonging to Crude Distillation Unit. The fluctuating value of temperature is reduced averagely by 57.1% compared with the non-decoupling control strategy and the mean absolute percentage error is within 0.02 under different operating conditions. The results show that the proposed decoupling control method has excellent decoupling performance and can improve the control performance of the system.

Research on pure azimuth passive positioning of unmanned aerial vehicle formation in electromagnetic silence environment

In the electromagnetic silence environment, for the azimuth-only passive localization problem in the conical formation, it was concluded that there was a deviation between the ideal standard formation and the actual formation. These disturbance deviations should be eliminated to make the UAV reach the ideal formation state. Therefore, the adjustment model of individual UAV, the directed graph model of formation node and the MDP model of adjustment strategy are constructed. Based on the relevant factor model constructed, the azimuth-only passive localization model in conical formation is established and solved in MATLAB. Finally, experiments and analysis are carried out in the simulation environment, and the effectiveness and feasibility of the proposed algorithm are proved.

Missile Fault Detection and Localization Based on HBOS and Hierarchical Signed Directed Graph

The rudder surfaces and lifting surfaces of a missile are utilized to acquire aerodynamic forces and moments, adjust the missile’s attitude, and achieve precise strike missions. However, the harsh flying conditions of missiles make the rudder surfaces and lifting surfaces susceptible to faults. In practical scenarios, there is often a scarcity of fault data, and sometimes, it is even difficult to obtain such data. Currently, data-driven fault detection and localization methods heavily rely on fault data, posing challenges for their applicability. To address this issue, this paper proposes an HBOS (Histogram-Based Outlier Score) online fault-detection method based on statistical distribution. This method generates a fault-detection model by fitting the probability distribution of normal data and incorporates an adaptive threshold to achieve real-time fault detection. Furthermore, this paper abstracts the interrelationships between the missile’s flight states and the propagation mechanism of faults into a hierarchical directed graph model. By utilizing bilateral adaptive thresholds, it captures the first fault features of each sub-node and determines the fault propagation effectiveness of each layer node based on the compatibility path principle, thus establishing a fault inference and localization model. The results of semi-physical simulation experiments demonstrate that the proposed algorithm is independent of fault data and exhibits high real-time performance. In multiple sets of simulated tests with randomly parameterized deviations, the fault-detection accuracy exceeds 98% with a false-alarm rate of no more than 0.31%. The fault-localization algorithm achieves an accuracy rate of no less than 97.91%.

DGEKT: A Dual Graph Ensemble Learning Method for Knowledge Tracing

Knowledge tracing aims to trace students’ evolving knowledge states by predicting their future performance on concept-related exercises. Recently, some graph-based models have been developed to incorporate the relationships between exercises to improve knowledge tracing, but only a single type of relationship information is generally explored. In this article, we present a novel Dual Graph Ensemble learning method for Knowledge Tracing (DGEKT), which establishes a dual graph structure of students’ learning interactions to capture the heterogeneous exercise–concept associations and interaction transitions by hypergraph modeling and directed graph modeling, respectively. To combine the dual graph models, we introduce the technique of online knowledge distillation. This choice arises from the observation that, while the knowledge tracing model is designed to predict students’ responses to the exercises related to different concepts, it is optimized merely with respect to the prediction accuracy on a single exercise at each step. With online knowledge distillation, the dual graph models are adaptively combined to form a stronger ensemble teacher model, which provides its predictions on all exercises as extra supervision for better modeling ability. In the experiments, we compare DGEKT against eight knowledge tracing baselines on three benchmark datasets, and the results demonstrate that DGEKT achieves state-of-the-art performance.

Determining Maximum Allowable Current of an RBS Using a Directed Graph Model and Greedy Algorithm

Reconfigurable battery systems (RBSs) provide a promising alternative to traditional battery systems due to their flexible and dynamically changeable topological structures that can be adapted to different battery charging and discharging strategies. A critical system parameter known as the maximum allowable current (MAC) is pivotal to RBS operation. This parameter is instrumental in maintaining the current of each individual battery within a safe range and serves as a guiding indicator for the system’s reconfiguration, ensuring its safety and reliability. This paper proposes a method for calculating the MAC of an arbitrary RBS using a greedy algorithm in conjunction with a directed graph model of the RBS. Using the shortest path of the battery, the greedy algorithm transforms the exhaustion of the switch states in the brute-force algorithm or variable search without utilizing structures in the heuristic algorithms in the combination of the shortest paths. The directed graph model, based on an equivalent circuit, provides a specific method for calculating the MAC of a given structure. The proposed method is validated using 2 previously published RBS structures and an additional one with a more complex structure. The results are the same as those from the brute-force algorithm, but the proposed method substantially improves the computational efficiency, being theoretically N s 2 N s − N b log 10 N b times faster than the brute-force algorithm for an RBS with N b batteries and N s switches. Another advantage of the proposed method is its ability to calculate the MAC of RBSs with arbitrary structures and variable batteries, even in scenarios with random isolated batteries.

Spatio-temporal data prediction of multiple air pollutants in multi-cities based on 4D digraph convolutional neural network.

In response to the problem that current multi-city multi-pollutant prediction methods based on one-dimensional undirected graph neural network models cannot accurately reflect the two-dimensional spatial correlations and directedness, this study proposes a four-dimensional directed graph model that can capture the two-dimensional spatial directed information and node correlation information related to multiple factors, as well as extract temporal correlation information at different times. Firstly, A four-dimensional directed GCN model with directed information graph in two-dimensional space was established based on the geographical location of the city. Secondly, Spectral decomposition and tensor operations were then applied to the two-dimensional directed information graph to obtain the graph Fourier coefficients and graph Fourier basis. Thirdly, the graph filter of the four-dimensional directed GCN model was further improved and optimized. Finally, an LSTM network architecture was introduced to construct the four-dimensional directed GCN-LSTM model for synchronous extraction of spatio-temporal information and prediction of atmospheric pollutant concentrations. The study uses the 2020 atmospheric six-parameter data of the Taihu Lake city cluster and applies canonical correlation analysis to confirm the data's temporal, spatial, and multi-factor correlations. Through experimentation, it is verified that the proposed 4D-DGCN-LSTM model achieves a MAE reduction of 1.12%, 4.91%, 5.62%, and 11.67% compared with the 4D-DGCN, GCN-LSTM, GCN, and LSTM models, respectively, indicating the good performance of the 4D-DGCN-LSTM model in predicting multiple types of atmospheric pollutants in various cities.

The storage capacity of a directed graph and nodewise autonomous, ubiquitous learning.

The brain, an exceedingly intricate information processing system, poses a constant challenge to memory research, particularly in comprehending how it encodes, stores, and retrieves information. Cognitive psychology studies memory mechanism from behavioral experiment level and fMRI level, and neurobiology studies memory mechanism from anatomy and electrophysiology level. Current research findings are insufficient to provide a comprehensive, detailed explanation of memory processes within the brain. Numerous unknown details must be addressed to establish a complete information processing mechanism connecting micro molecular cellular levels with macro cognitive behavioral levels. Key issues include characterizing and distributing content within biological neural networks, coexisting information with varying content, and sharing limited resources and storage capacity. Compared with the hard disk of computer mass storage, it is very clear from the polarity of magnetic particles in the bottom layer, the division of tracks and sectors in the middle layer, to the directory tree and file management system in the high layer, but the understanding of memory is not sufficient. Biological neural networks are abstracted as directed graphs, and the encoding, storage, and retrieval of information within directed graphs at the cellular level are explored. A memory computational model based on active directed graphs and node-adaptive learning is proposed. First, based on neuronal local perspectives, autonomous initiative, limited resource competition, and other neurobiological characteristics, a resource-based adaptive learning algorithm for directed graph nodes is designed. To minimize resource consumption of memory content in directed graphs, two resource-occupancy optimization strategies-lateral inhibition and path pruning-are proposed. Second, this paper introduces a novel memory mechanism grounded in graph theory, which considers connected subgraphs as the physical manifestation of memory content in directed graphs. The encoding, storage, consolidation, and retrieval of the brain's memory system correspond to specific operations such as forming subgraphs, accommodating multiple subgraphs, strengthening connections and connectivity of subgraphs, and activating subgraphs. Lastly, a series of experiments were designed to simulate cognitive processes and evaluate the performance of the directed graph model. Experimental results reveal that the proposed adaptive connectivity learning algorithm for directed graphs in this paper possesses the following four features: (1) Demonstrating distributed, self-organizing, and self-adaptive properties, the algorithm achieves global-level functions through local node interactions; (2) Enabling incremental storage and supporting continuous learning capabilities; (3) Displaying stable memory performance, it surpasses the Hopfield network in memory accuracy, capacity, and diversity, as demonstrated in experimental comparisons. Moreover, it maintains high memory performance with large-scale datasets; (4) Exhibiting a degree of generalization ability, the algorithm's macroscopic performance remains unaffected by the topological structure of the directed graph. Large-scale, decentralized, and node-autonomous directed graphs are suitable simulation methods. Examining storage problems within directed graphs can reveal the essence of phenomena and uncover fundamental storage rules hidden within complex neuronal mechanisms, such as synaptic plasticity, ion channels, neurotransmitters, and electrochemical activities.

The Construction of Satisfaction Evaluation System of Tourism Scenic Area Management Based on Cognitive Mapping Construct

Abstract Building a scenic satisfaction evaluation system is an important initiative to improve the quality of tourism management. In this paper, an improved ontology modeling method is used to construct the ontology of the tourism domain, and operations such as denoising and de-duplication are used to process the ontology data while a data dictionary of entities is established. Oriented to tourism-named entities, the identification of entities is completed based on a directed graph model, and the evaluation index system of scenic spot satisfaction is constructed accordingly. For the research sample of the ancient village scenic spot, the importance of indicators F3, F5, F8, and F15 are 3.68, 4.20, 4.18, and 4.32, respectively, and the performance is 3.75, 4.06, 4.13, and 4.18, respectively. The satisfaction evaluation index established based on cognitive mapping reflects the validity.

Structural learning of functional directed graphical models with incomplete signals

Functional directed graph model (DGM) learning has been widely used to analyze complex systems. Most existing works assume that the functional signals are complete, which in reality is not true. To address this problem, in this study, a framework for DGM learning with incomplete signals is proposed. Specifically, a penalty term that integrates information from the graph structure is added to the Maximum Margin Matrix Factorization (MMMF) objective function. The proposed method can be used with a known structure to estimate the functional relationship between nodes or with an unknown structure to estimate the relationship together with the graph structure. Numerical experiments and a real-world case study of monocrystalline silicone manufacturing are performed to verify the effectiveness of the proposed method when the signal matrices are incomplete.

Fault Location of Power Battery System Based on Directed Graph Model

As the core part of the electric ship, the power battery system is the fault-prone area of the whole ship due to the harsh working environment and complex structure. This paper uses the method based on the directed graph model to build the directed graph model of the ship’s power battery system with the module as the basic unit to achieve the fault location of the ship’s power battery system at the module level and carries out simulation experiments to prove the feasibility of the scheme.

Spatio-temporal graph convolutional networks driven by data-physical fusion for parameter prediction of natural gas dehydration system

Triethylene glycol dehydration unit is a piece of essential device for removing moisture from raw natural gas during natural gas production. However, the existing station equipment management systems are mostly collection-oriented with little analysis, lack the effective methods of parameter prediction and fault warning, and the strong coupling between the monitoring parameters is a problem should be study. To solve these problems, this paper analyzes the time dependence and spatial correlation of these parameters. Also, a spatio-temporal graph convolutional networks prediction model driven by data-physical fusion (SG-STGCN) is proposed for constructing the graph structure. Firstly, the signed directed graph model is established based on the physical process, and the weight of each edge is obtained by using the grey relational analysis (GRA). Secondly, by stacking spatio-temporal convolutional modules, the temporal and spatial dependencies over a long range of time are captured to realize multivariate parameter prediction. Then, the real-time monitoring data of a dehydration station are used for analysis. The experimental results showed that the proposed method can achieves the best predict result compared with other methods, and can be used in the fault early warning to maintain high reliability of equipment. Finally, the SG-STGCN has been integrated and tested successfully on the real-time monitoring platform of a dehydration unit.

Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, the underlying network in many studies is assumed to be undirected. Although the directed graph model is rarely adopted, it is more appropriate for many applications, especially for real-world networks. In this paper, we present a general framework for extending graph signal processing to directed graphs in the graph fractional domain. For this purpose, we consider a new definition for the fractional Hermitian Laplacian matrix on a directed graph and generalize the spectral graph fractional Fourier transform to the directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used to reduce unnecessary noise superimposed on real data. Finally, the denoising performance of the proposed DGFRFT approach is also evaluated through numerical experiments by using real-world directed graphs.

The Rank of the Sandpile Group of Random Directed Bipartite Graphs

We identify the asymptotic distribution of p-rank of the sandpile group of random directed bipartite graphs which are not too imbalanced. We show this matches exactly with that of the Erdös–Rényi random directed graph model, suggesting that the Sylow p-subgroups of this model may also be Cohen–Lenstra distributed. Our work builds on the results of Koplewitz who studied p-rank distributions for unbalanced random bipartite graphs, and showed that for sufficiently unbalanced graphs, the distribution of p-rank differs from the Cohen–Lenstra distribution. Koplewitz (sandpile groups of random bipartite graphs, https://arxiv.org/abs/1705.07519, 2017) conjectured that for random balanced bipartite graphs, the expected value of p-rank is O(1) for any p. This work proves his conjecture and gives the exact distribution for the subclass of directed graphs.

LaSCA: A Visualization Analysis Tool for Microstructure of Complex Systems

Over the past few decades, plenty of visualization software for the structural analysis of disordered/complex systems has been developed, but the uniqueness and correctness of structural quantification for such systems are still challenging. This paper introduces a visualization analysis tool based on the largest standard cluster analysis (LaSCA), which satisfies the three essential requirements for general structural analysis: physical correctness, objective identification, and injective representation. The specific functionalities of LaSCA include the directed graph model of complex systems, novel structural parameters, topologically close-packed structures, arbitrary partial pair distribution functions, the identification of long-range ordered structures, the adaptive selection of graphical elements, the tracking display of atom ID, user-defined view angles, various options for atom selection, and so on. The program is efficiently based on OpenGL hardware acceleration, employing special algorithms to treat bonds as cylinders or lines and treat atoms as spheres, icosahedrons, tetrahedrons, or points. LaSCA can process more than 1.2 million atoms within 50 s on a PC with 1 GB memory and four cores (Intel Core i7-9700). It is robust and low-cost for surveying short-, medium-, and long-range ordered structures and tracking their evolutions.

Joint Sampling and Reconstruction of Time-Varying Signals Over Directed Graphs

Vertex-domain and temporal-domain smoothness of time-varying graph signals are cardinal properties that can be exploited for effective graph signal reconstruction from limited samples. However, existing approaches are not directly applicable when the signal's frequency occupancy changes with time. Moreover, while e.g., sensor network applications can benefit from directed graph models, the non-orthogonality of the graph eigenvectors can challenge spectral-based signal reconstruction algorithms. In this context, here we consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -sparse time-varying signals with unknown frequency supports. By exploiting the smoothness of the varying graph frequency supports and employing shift operations over directed graphs, we study joint sampling of multiple varying signals based on Schur decomposition to reconstruct each signal by orthogonal frequency components. Firstly, joint frequency support of the multiple signals is identified by proposing a two-stage Individual-Joint sampling scheme. Based on the estimated frequency support, the GFT coefficients of each signal can be recovered using data collected in individual sampling stage. Greedy algorithms are proposed for vertex set selection and graph shift order selection, which enable a robust signal reconstruction against additive noise. Considering the signals in applications may be approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -sparse, we further exploit the samples in both individual and joint sampling stages and investigate the optimal signal reconstruction as a convex optimization problem with adaptive frequency support selection. The proposed optimal sampling and reconstruction algorithms outperform several existing schemes in random network and sensor network data gathering.

A novel integrated fault diagnosis method of chemical processes based on deep learning and information propagation hysteresis analysis

BackgroundTo guarantee the stationary operation of chemical plant, the anomaly symptoms of equipment should be discovered as soon as possible. Due to the limited ability of single fault diagnosis method in the increasingly complex industrial process, the integration of different methods has become a hot research direction. MethodsA three-layer fusion fault diagnosis method is proposed in this paper. This method consists of three layers. Time domain features of time series process variables are first extracted by sliding window. Then, the bidirectional long short-term memory network based on time domain feature extraction (T-BiLSTM) is formed to accomplish the online fault identification task. At last, the causalities of fault variables are obtained based on improved signed directed graph model with dynamic time warping (TD-SDG) to locate the fault sources. FindingsThe application to Tennessee Eastman (TE) shows that the average false positive rate (FPR) of T-BiLSTM is 1.98%, and the average fault diagnosis rate (FDR) is 96.6%. TD-SDG model realizes fault inference and location. This novel integrated fault diagnosis method thus can identify fault types and locate fault sources quickly based on graphical scenario object model with a high application capacity.

Вершинно-зважена гіпотеза Сеймура

Seymour's conjecture is one of the most famous unsolved mathematical problems in graph theory, which was formulated by Paul Seymour in 1990. This problem is also known as the «second neighborhood problem». A directed graph models a social network in which no two people knoweach other at the same time. This conjecture states that there will be at least one person for whom acquaintances of acquaintances will be no less than ac-quaintances. Definitions and basic theorems of graph theory are described in [1-3]. For an arbitrary graph, Seymour's hypothesis remains unsolved, but there are already proofs for partial cases and for some types of graphs, which are given in [4-6].Seacrest Tyler [5] investigated Seymour's conjecture for graphs with weighted arcs.In [6] showed that every simple digraph without loops or digons con-tains a vertexvfor which the second neighborhood is greater than or equal to the first multiplied by a certain constant.In [7] provided sufficient conditions under which there must exist some vV(D), as wellas examine properties of a minimal graph which does not have such a vertex. We show that if one such graph exists, then there exist in-finitely many strongly-connected graphs having no such vertex.The relevance of the chosen research topic is determined by the rapid pace of development of modern graph theory, which is associated with the expansion of its scope of use: business, logistics, tourism and, most im-portantly, modeling of various networks. One extension of the conjecture is to consider vertex-weighted di-graphs. In this paper we introduce a version of the conjecture for vertex-weighted digraphs and proved that the Seymour conjecture is equivalent to conjecture for vertex-weighted digraphs.

Planning of Obstacle-Aided Navigation for Multi-Legged Robots Using a Sampling-Based Method Over Directed Graphs

Existing work in legged robot navigation in cluttered environments often seeks collision-free paths that avoid obstacle interactions. Here we present a new approach for multi-legged robots to utilize leg-obstacle collisions to generate desired dynamics. To predict the change of robot state under repeated leg-obstacle collisions, we construct a discretized directed graph model: each node of the graph represents a different robot state, whereas the directed edges pointing from one node to another represent the transitions from one robot state to the next within one stride. These obstacle-modulated state transitions can depend on the robot gaits used. To capture this dependence, an empirical interaction model is used to compute the change of robot state based on initial contact positions between robot legs and obstacles. To validate the prediction of robot state transitions, we experimentally measure the state of a quadrupedal robot as it traverses a periodic obstacle field with three different gaits: bound, trot, and pace. We observed that the robot could passively converge to different steady state orientations, and these steady states corresponded well with the Strongly-Connected-Path-Components (SCPCs) within the directed graph. Searching over the graph for connected paths of SCPCs allows development of a gait planner that can generate gait switching strategies for a robot to achieve desired states by simply engaging with a sequence of leg-obstacle collisions. We demonstrate in experiments that using this method an open-loop quadrupedal robot was able to achieve desired orientations within a periodic obstacle field without any sensory input or active steering.

Dynamic Resource Orchestration for Service Capability Maximization in Fog-Enabled Connected Vehicle Networks

Technological advances in fog computing are precipitating an evolution in conventional vehicle networks to a new paradigm called fog-enabled connected vehicle networks (FCVNs). FCVNs provide communication efficiency for ensuring safe transportation through the massive Internet of vehicles. In FCVNs, massive vehicles tend to associate with roadside units and high power nodes, which act as fog nodes (FNs), when they have a good channel quality and/or popular contents. This circumstance may lead to a load imbalance among the FNs. This problem significantly decreases the resource utilization efficiency and service capability of the networks. In this article, we propose a dynamic resource orchestration (DRO) scheme to harmonize resource allocation for connected vehicles by migrating the offloaded services among FNs. A graph-theoretic approach is utilized to transform the FCVN into a directed graph model, where the maximum resource reduction obtained by service migrations is considered the weight of the link between every two FNs. Subsequently, the maximum weight matching solution is used to determine optimal pairs of FNs for migrating services to maximize network resource utilization. Our simulation results reveal that the proposed DRO scheme achieves significant improvements in terms of service capability, throughput, and resource utilization efficiency as compared with existing algorithms.